Question

How many solutions does the system of linear equations have?Use the drop-down menus to explain your answer.Y= 3/4x+ 12y= 4/3xThe system of linear equations will have A. No solutionB. Exactly one solutionC. Infinitely solutionsbecause the slopes of the equations areA. The sameB. Different so the fines will A. Not intersect at allB. Intersect at one point C. Both be the same linePS: If too much or difficult you can just say the full sentence correctly

Answer 1

Substitute 4/3x for y in the equation y=3/4x+12 to obtain the value of x.

$\begin{gathered} \frac{4}{3}x=\frac{3}{4}x+12 \\ \frac{4}{3}x-\frac{3}{4}x=12 \\ \frac{16x-9x}{12}=12 \\ x=\frac{144}{7} \end{gathered}$

Substitute 144/7 for x in equation y=4/3 x to obtain the value of y.

$\begin{gathered} y=\frac{4}{3}\cdot\frac{144}{7} \\ =\frac{192}{7} \end{gathered}$

So, the equation have unique solution or exactly one solution because the slopes of the equations are different so the fines will intersect at one point.